Quantum Physics

936 Chapter 28 Atomic PhysicsSection 28.9 The Exclusion Principle andthe Periodic Table36. (a) Write out the electronic configuration of theground state for oxygen (Z 8). (b) Write out thevalues for the set of quantum numbers n, , m , andm s for each of the electrons in oxygen.37.Two electrons in the same atom have n 3 and 1. (a) List the quantum numbers for the possiblestates of the atom. (b) How many states wouldbe possible if the exclusion principle did not applyto the atom?38. How many different sets of quantum numbers arepossible for an electron for which (a) n 1,(b) n 2, (c) n 3, (d) n 4, and (e) n 5?Check your results to show that they agree with thegeneral rule that the number of different sets ofquantum numbers is equal to 2n 2 .39. Zirconium (Z 40) has two electrons in an incompleted subshell. (a) What are the values of n and for each electron? (b) What are all possible valuesof m and m s ? (c) What is the electron configurationin the ground state of zirconium?Section 28.10 CharacteristicX-Rays40. The K-shell ionization energy of copper is 8 979 eV.The L-shell ionization energy is 951 eV. Determinethe wavelength of the K emission line of copper.What must the minimum voltage be on an x-raytube with a copper target in order to see the K line?41. The K x-ray is emitted when an electron undergoesa transition from the L shell (n 2) to the K shell(n 1). Use the method illustrated in Example 28.5to calculate the wavelength of the K x-ray from anickel target (Z 28).42. When an electron drops from the M shell (n 3)to a vacancy in the K shell (n 1), the measuredwavelength of the emitted x-ray is found to be0.101 nm. Identify the element.43. The K series of the discrete spectrum of tungstencontains wavelengths of 0.018 5 nm, 0.020 9 nm,and 0.021 5 nm. The K-shell ionization energy is69.5 keV. Determine the ionization energies of theL, M, and N shells. Sketch the transitions that producethe above wavelengths.ADDITIONAL PROBLEMS44. In a hydrogen atom, what is the principle quantumnumber of the electron orbit with a radius closest to1.0 m?45. (a) How much energy is required to cause an electronin hydrogen to move from the n 1 state tothe n 2 state? (b) If the electrons gain this energyby collision between hydrogen atoms in ahigh-temperature gas, find the minimum temperatureof the heated hydrogen gas. The thermal energyof the heated atoms is given by 3k B T/2, wherek B is the Boltzmann constant.46. A pulsed ruby laser emits light at 694.3 nm. For a14.0-ps pulse containing 3.00 J of energy, find (a)the physical length of the pulse as it travels throughspace and (b) the number of photons in it. (c) Ifthe beam has a circular cross section 0.600 cm in diameter,find the number of photons per cubic millimeter.47. The Lyman series for a (new?) one-electron atomis observed in a distant galaxy. The wavelengths ofthe first four lines and the short-wavelength limitof this Lyman series are given by the energy-leveldiagram in Figure P28.47. Based on this information,calculate (a) the energies of the groundstate and first four excited states for this oneelectronatom and (b) the longest-wavelength (alpha)lines and the short-wavelength series limit inthe Balmer series for this atom.ENERGYn = ∞n = 5n = 4n = 3n = 2n = 1= 202.6 nmλ= 170.9 nmλ= 162.1 nmλFigure P28.47= 158.3 nmλ= 152.0 nmλE ∞ = 0E 5E 4E 3E 2E 1